The significance of the result lies in how it sidesteps the central limitation of conventional photonic graph-state synthesis. In linear optical systems, the standard tool for combining smaller resource states into bigger ones is the fusion operation, a divide-and-conquer strategy first formalized by Browne and Rudolph in 2005. Fusion works by interfering photons and measuring the outcomes, which links the constituent states into a larger graph. The catch is probability: with ordinary beam splitters and detectors, fusion succeeds only some of the time. Failed attempts destroy the participating photons, forcing experimenters to build elaborate multiplexing schemes, extensive feed-forward electronics, and massive hardware overheads simply to make the overall process behave deterministically. Resource-cost analyses, such as the 2015 study by Li and colleagues, have quantified how punishing these overheads become for fault-tolerant linear optical quantum computing.

The Tsinghua group, led by Hongyi Zhang and Luming Duan of the Center for Quantum Information at the Institute for Interdisciplinary Information Sciences, took a different route. Rather than relying on passive linear optics, they implemented the fusion operation on a superconducting circuit device, where microwave photons interact with engineered quantum circuits in a controllable, coherent way. Their scheme non-destructively projects pairs of flying microwave photons into Bell states, the maximally entangled two-qubit states that serve as the connective tissue of graph-state fusion. Because the projection is deterministic and the photons survive the operation, every fusion attempt contributes to the final state, eliminating the exponential losses that plague probabilistic protocols.

The photons themselves are encoded in time bins, a format in which the logical states of a qubit are represented by a photon arriving in one of two well-defined temporal modes. Time-bin encoding is attractive for propagating qubits because it is robust against many channel imperfections and fits naturally with sequential generation schemes. The team generated small time-bin-encoded cluster states on demand, meaning that each elementary building block could be produced precisely when the protocol required it. On-demand availability is crucial for a scalable architecture: if the photonic qubits must wait in flight while the apparatus catches up, decoherence erodes the fragile quantum correlations before the graph can be completed.

Managing decoherence is, in fact, a central theme of the experiment. Superconducting qubits, the stationary quantum circuits that mediate the photon-photon interactions, have finite coherence times, and a long graph-state synthesis sequence would normally exhaust them. The researchers therefore built active reset and reuse of the superconducting qubits into the protocol. After each qubit has performed its role in generating or fusing photonic qubits, it is rapidly reset to a known state and pressed back into service. This recycling circumvents the effects of decoherence that would otherwise accumulate over the many rounds of photon emission and fusion needed to build a large graph, and it echoes the complete methods sets developed in other platforms, such as the scalable ion trap techniques demonstrated by Home and colleagues in 2009.

Programmability is the second pillar of the demonstration. Because the fusion operation can be applied selectively to chosen pairs of photonic qubits, the same hardware can produce different graph topologies under software control. The team showed this by fusing two linear cluster states of three qubits each, joining qubit 2 and qubit 4 to create a new vertex and thereby producing a five-vertex caterpillar graph state, a structure whose entanglement pattern resembles a chain with additional rungs. Verifying such states is itself a formidable task: full quantum state tomography of a five-qubit density matrix would be prohibitively costly because of the sheer dimension of the Hilbert space, so the experimenters instead measured a subset of stabilizer operators, the commuting observables that uniquely characterize stabilizer states such as graph states. One stabilizer, involving Z and X operators across all five qubits, was deliberately omitted from the measurement set for exactly this reason.

To certify that the generated states were genuinely multipartite entangled, meaning that the entanglement cannot be reduced to any mixture of states over smaller partitions, the team computed fidelities with respect to the ideal target states and compared them against the standard threshold of 0.5. The measurements, performed with datasets of five times ten to the seventh power shots and analyzed with bootstrap standard errors derived by parametric resampling, confirmed genuine multipartite entanglement. Pushing further through repetitive fusion, the researchers scaled the approach to 13 photonic qubits, establishing what they describe as a scalable framework for photonic graph-state synthesis. The stabilizer formalism used for entanglement detection draws on well-established tools, including the entanglement-witness techniques of Toth and Guhne.

The microwave domain in which this demonstration takes place deserves particular attention. Circuit quantum electrodynamics has matured into a platform where itinerant microwave photons can be generated, routed, and measured with high fidelity, and where quantum non-demolition detection of individual propagating photons became possible in 2018 through the work of Kono and colleagues and Besse and colleagues. Deterministic quantum state transfer and remote entanglement using microwave photons were demonstrated by Kurpiers and colleagues in 2018, and universal gate sets for itinerant microwave photons followed in 2022. The Tsinghua result extends this trajectory from point-to-point operations to the synthesis of extended entangled photonic structures, a capability that connects naturally to proposals for microwave quantum networks and to hybrid architectures in which superconducting processors interface with flying qubits.

At the same time, the achievement sits within a broader international effort to make photonic graph states deterministic. Single quantum emitters, including quantum dots, trapped atoms in optical cavities, Rydberg superatoms, and solid-state emitters, have all been used to generate cluster states sequentially, with notable demonstrations by Cogan and colleagues, Thomas and colleagues, and Yang and colleagues between 2022 and 2025. Thomas, Ruscio, Morin, and Rempe showed in 2024 that deterministically generated photonic graph states from a single atom can themselves be fused, and temporal fusion of emitter-produced resource states was reported in 2025. The Tsinghua experiment adds a distinct architectural idea to this landscape: instead of growing one large state from a single emitter, it fuses independently generated small states through a deterministic Bell-state projection, combining the strengths of on-demand sources with the modularity of fusion-based quantum computation, a model formalized by Bartolucci and colleagues in 2023.

The implications reach toward several long-sought applications. Measurement-based quantum computing, proposed by Raussendorf and Briegel in 2001 as the one-way quantum computer, consumes a large entangled graph state as its computational substrate, and fusion-based schemes with high fault-tolerance thresholds have been proposed for one-dimensional cluster states. All-photonic quantum repeaters, introduced by Azuma, Tamaki, and Lo in 2013, replace matter-based quantum memories with graph states, removing the memory bottlenecks of conventional repeater chains. Graph states also serve as resources for quantum metrology, as Shettell and Markham showed in 2020. A deterministic, programmable fusion engine that can be reconfigured at will brings each of these visions closer to practical realization, particularly if the underlying photonic qubits can eventually be converted to the optical telecom band for long-distance distribution. The work was supported by China’s Quantum Science and Technology major project, the National Natural Science Foundation of China, Tsinghua University, and the Ministry of Education, and the underlying data have been made openly available, offering the community a concrete foundation on which to build the next generation of entangled photonic resources.

Subject of Research: Deterministic fusion of microwave photons on superconducting circuits for scalable photonic graph-state generation

Article Title: Deterministic and programmable fusion for the scalable generation of photonic graph states

Article References: Li, Y., Yang, Y., Bao, Z., Yang, J., Sun, L., Song, Y., Wu, Y., Zhang, H., & Duan, L. (2026). Deterministic and programmable fusion for the scalable generation of photonic graph states. Nature Physics. https://doi.org/10.1038/s41567-026-03471-5

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03471-5

Keywords: photonic graph states, quantum entanglement, superconducting qubits, microwave photons, fusion operation, cluster states, measurement-based quantum computing, quantum repeaters, time-bin encoding, circuit quantum electrodynamics, stabilizer measurements, genuine multipartite entanglement